Abstract
A method is presented that is capable of following discontinuities in the solution of hyperbolic partial differential equations. At every time step for each cell in the neighborhood of the discontinuity, the fraction of the cell lying behind the discontinuity curve is updated. From this data the front is reconstructed. The method is applied to three scalar differential equations: inviscid Burgers' equation, the Buckley-Leverett equation for immiscible porous flow, and the equation for two-phase miscible flow in a porous medium.
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